27.2 Huygens's Principle: Diffraction
Which of the following statements is true about Huygens’s principle of secondary wavelets?
- It can be used to explain the particle behavior of waves.
- It states that each point on a wavefront can be considered a new wave source.
- It can be used to find the velocity of a wave.
- All of the above.
Explain why the amount of bending that occurs during diffraction depends on the width of the opening through which light passes.
27.3 Young’s Double Slit Experiment
Superposition of which of the following light waves may produce interference fringes? Select two answers.
Wave1 = A1sin(2ωt)
Wave2 = A2sin(4ωt)
Wave3 = A3sin(2ωt + θ)
Wave4 = A4sin(4ωt + θ).
- Wave1 and Wave2
- Wave2 and Wave4
- Wave3 and Wave1
- Wave4 and Wave3
In a double slit experiment with monochromatic light, the separation between the slits is 2 mm. If the screen is moved by 100 mm toward the slits, the distance between the central bright line and the second bright line changes by 32 μm. Calculate the wavelength of the light used for the experiment.
In a double slit experiment, a student measures the maximum and minimum intensities when two waves with equal amplitudes are used. The student then doubles the amplitudes of the two waves and performs the measurements again. Which of the following will remain unchanged?
- The intensity of the bright fringe
- The intensity of the dark fringe
- The difference in the intensities of consecutive bright and dark fringes
- None of the above
Draw a figure to show the resultant wave produced when two coherent waves (with equal amplitudes x) interact in phase. What is the amplitude of the resultant wave? If the phase difference between the coherent waves is changed to 60º, what will be new amplitude?
What will be the amplitude of the central fringe if the amplitudes of the two waves in a double slit experiment are a and 3a?
If the ratio of amplitudes of the two waves in a double slit experiment is 3:4, calculate the ratio of minimum intensity (dark fringe) to maximum intensity (bright fringe).
27.4 Multiple Slit Diffraction
Which of the following cannot be a possible outcome of passing white light through several evenly spaced parallel slits?
- The central maximum will be white but the higher-order maxima will disperse into a rainbow of colors.
- The central maximum and higher-order maxima will be of equal widths.
- The lower wavelength components of light will have less diffraction compared to higher wavelength components for all maxima except the central one.
- None of the above.
White light is passed through a diffraction grating to a screen some distance away. The nth-order diffraction angle for the longest wavelength (760 nm) is 53.13º. Find the nth-order diffraction angle for the shortest wavelength (380 nm). What will be the change in the two angles if the distance between the screen and the grating is doubled?
27.5 Single Slit Diffraction
A diffraction pattern is formed on a screen when light of wavelength 410 nm is passed through a single slit of width 1 μm. If the source light is replaced by another light of wavelength 700 nm, what should be the width of the slit so that the new light produces a pattern with the same spacing?
- 0.6 μm
- 1 μm
- 1.4 μm
- 1.7 μm
Monochromatic light passing through a single slit forms a diffraction pattern on a screen. If the second minimum occurs at an angle of 15º, find the angle for the fourth minimum.
27.6 Limits of Resolution: The Rayleigh Criterion
What is the relationship between the width (W) of the central diffraction maximum formed through a circular aperture and the size (S) of the aperture?
- W increases as S increases.
- W decreases as S increases.
- W can increase or decrease as S decreases.
- W can neither increase nor decrease as S decreases.
Light from two sources passes through a circular aperture to form images on a screen. State the Rayleigh criterion for the images to be just resolvable and draw a figure to visually explain it.
27.7 Thin Film Interference
Which of the following best describes the cause of thin film interference?
- Light reflecting from a medium having an index of refraction less than that of the medium in which it is traveling.
- Light reflecting from a medium having an index of refraction greater than that of the medium in which it is traveling.
- Light changing its wavelength and speed after reflection.
- Light reflecting from the top and bottom surfaces of a film.
A film of magnesium fluoride (n = 1.38) is used to coat a glass camera lens (n = 1.52). If the thickness of the film is 105 nm, calculate the wavelength of visible light that will have the most limited reflection.
Which of the following statements is true for the direction of polarization for a polarized light wave?
- It is parallel to the direction of propagation and perpendicular to the direction of the electric field.
- It is perpendicular to the direction of propagation and parallel to the direction of the electric field.
- It is parallel to the directions of propagation and the electric field.
- It is perpendicular to the directions of propagation and the electric field.
In an experiment, light is passed through two polarizing filters. The image below shows the first filter and axis of polarization.
The intensity of the resulting light (after the first filter) is recorded as I. Three configurations (at different angles) are set up for the second filter, and the intensity of light is recorded for each configuration. The results are shown in the table below:
|Set up||Angle of second filter compared to first filter||Intensity of light after second filter|
Complete the table by calculating θ1, θ2, and θ3.